For the purpose of this conversation, I think if you have 34 putts a round, spending time learning how to putt side saddle is going to be an ineffective use of your time and resources (assuming you are limited in practice time and cash). Dropping your average to 33 putts a round will drop your handicap by 1 stroke.
Greens in Regulation is regularly tied directly to handicap, but it doesn’t necessarily tell the full story of where you need to improve. Average putts a round is also an incomplete picture (I was more using it to illustrate that there is only a 2 putt difference between a scratch golfer and a 10 handicap…)
Honestly if you want to improve, I think the first place to look is overall strategy. The first step to that is to look at where you are “leaking” shots… If you are averaging 34 putts, you aren’t losing anything on the green, so I wouldn’t focus your attention there, especially if you aren’t 3 putting.
Major Leak points, as far as I’m concerned (I’m just an internet stranger who thinks about golf too much):
Off the Tee:
Are you hitting driver? If not, you need to get confidence in your driver and put the longest ball you can into play. This simply makes the game easier.
Are you hitting balls into hazards? Figure out your dispersion, and eliminate hazards from your usual shot dispersion… Aiming at the rough isn’t a bad strategy if it means you won’t lose a ball OB.
Have you eliminated the two way miss? This is more advanced, but if you are both hooking and slicing the ball, you are at a significant disadvantage. One way miss: myth? You won’t “eliminate” one side of the fairway, but you’ll at least know which direction your ball will usually go.
Recovery Shots: Are you taking your medicine and putting yourself in a position to putt for par? If you are in the trees, get out. If you are in a bad lie and have to carry a hazard to get to the green, consider punching out… In every situation there is “statistically” smart play that will get you to the hole in the fewest strokes. It’s usually not the hero shot of hooking a ball around the tree. Avoiding big numbers is the best way to lower your score… it’s not as much fun (for me) but it’s much smarter golf.
Shots into the green: What’s your target and what’s your aim? Do you know your dispersion? This one is both simple and hard… it’s something I’m actively working on. "Pin seeking’ is a losing strategy. Get the ball on the green. Take more club (most misses are short) and try to hit the center of the green (for the most part, I’m still learning this concept, but aiming at the center is the best decision 80% of the time). You are already a capable putter, so getting that club into your hand faster is going to lower your score.
Around the Green: To quote my father “Get out, get on, get close”. Once again, putting is better than chipping and the closer you are to the hole, the more likely you are to make the putt. Worry less about being “below the hole” and more about being close to the hole.
If you hit 9 greens in regulation and the other 9 in one extra stroke, 34 putts would be a 79 on a par 72… To me, that seems easier than 7 greens in regulation, 11 in one extra stroke and 32 putts for the same score.